Experiment 1

positive skew condition (400, 504, 636, 800, 1008, 1270, and 1600 ms)

negative skew condition (400, 730, 992, 1200, 1366, 1496, and 1600 ms)

Range Frequency Theory

To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the distribution of stimuli within the sets firstly.

sumfreq_exp1_sub1 <-  dat_exp1 %>% filter(NSub == 1) %>% group_by(cond, curDur) %>% summarise(count = n())
count_exp1 <- sum(sumfreq_exp1_sub1$count)/2
sumfreq_exp1_sub1$exp <- 'Exp1'
sumfreq_exp1_sub1$freq <- sumfreq_exp1_sub1$count/count_exp1*100

# rename columns
fig_exp1_sub1_dist <- ggplot(data=sumfreq_exp1_sub1, aes(x=curDur, y=count, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) +
   #geom_smooth(method="loess",se = FALSE)+
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
   scale_x_continuous(breaks=seq(0, 1600, 200)) +
    scale_color_manual(values = c('gray','black')) +
    scale_fill_manual(values = c('gray','black')) +mytheme+ facet_wrap(~cond)

fig_exp1_sub1_dist

if (saveFigure == TRUE){
  ggsave("figures/fig_exp1_sub1_dist.svg", fig_exp1_sub1_dist)
}

plot the distribution of stimulus set

mDist_exp1 <-  dat_exp1 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
summarise(m_cDur = mean(curDur), n = dplyr::n(),
cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp1

plot_mDist_exp1 <- ggplot(mDist_exp1,aes(cond, m_cDur, color = cond, fill = cond))+
geom_bar(stat='identity') +
geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
labs(x = " ", y = "Mean of Durations (ms)") +
scale_color_manual(values = c('gray','black')) +
scale_fill_manual(values = c('gray','black')) +
theme(legend.position = "none", legend.title = element_blank())+
theme(panel.grid.major=element_line(colour=NA))+
theme(axis.text.y = element_text(size=26,colour = "black"),
axis.text.x   = element_text(size=26, colour = "black"),
axis.title.y  = element_text(size=26, colour = "black"),
axis.title.x  = element_text(size=26, colour = "black"),
panel.background = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.line = element_line(colour = "black"))

if (saveFigure == TRUE){
ggsave("figures/plot_mDist_exp1.png", plot_mDist_exp1, 
       width = 4.5, height=5.5)
}
plot_mDist_exp1

fit psychometric functions

fits_exp1 = quickpsy(dat_exp1, x = curDur, k =RP, prob = .5,
                grouping = .(cond, NSub), thresholds = FALSE)

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head(fits_exp1$thresholds)
fits_exp1_all = quickpsy(dat_exp1, x = curDur, k =RP, prob = .5, grouping = .(cond))
fits_exp1_all
NULL
# plot fitted function
 plot_fit_exp1 <- plot(fits_exp1_all) +  
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
    scale_color_manual(values = c('gray','black')) +
    scale_fill_manual(values = c('gray','black')) +
    theme(legend.position = c(0.7, 0.2), legend.title = element_blank())
Ignoring unknown aesthetics: x
  plot_fit_exp1

  #+theme_classic()
if (saveFigure == TRUE){
  ggsave("figures/pse_exp1.png", plot_fit_exp1)
}
aic(fits_exp1_all)
ypred(fits_exp1_all)

======= ##slope From the equation of psychometric fuction (PF), we can easily obtained the point of subjective equality (PSE, \(\alpha\)) and just noticeable difference (JND). Notice, the JND is defined by the difference between thresholds P=0.5 and P=0.75, so we have \[JND = log3/ \beta\] Therefore,

\[\beta = 3 / e^{JND} \]

exp1_all_thres<- fits_exp1_all$thresholds
exp1_all_thres$slope = 3/exp(exp1_all_thres$thre/1000) #slope
exp1_all_thres
exp1_thres<- fits_exp1$thresholds
exp1_thres$slope = 3/exp(exp1_thres$thre/1000) #slope
exp1_thres

list all of the parameter for each subjects

par_exp1 = fits_exp1$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns
par_exp1$slope = 3/exp(par_exp1$jnd/1000) #slope

par_exp1
mpars_exp1 = par_exp1%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd),  m_slope = mean(slope), n = n(),
            pse_se = sd(pse)/sqrt(n-1), 
            jnd_se = sd(jnd)/sqrt(n-1),
            slope_se = sd(slope)/sqrt(n-1)) 

mpars_exp1

======= ##Export for JASP

List all of the parameters for exp1 and export data for JASP

exp1_jasp <- par_exp1%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(`PS`, c("PSC_pse", "PSC_jnd","PSC_slope"), sep = "_")%>%
  separate(`NS`, c("NSC_pse", "NSC_jnd","NSC_slope"), sep = "_")

exp1_jasp

plot PSE

plot_pse_exp1 <- ggplot(mpars_exp1,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
    geom_signif(comparisons=list(c("PS", "NS")), annotations="*", y_position = 1150, tip_length = 0, vjust=0.4, color = 'black') +
   labs(x = " ", y = "Mean PSE (ms)") +
  coord_cartesian(ylim = c(0,1300)) +
    scale_color_manual(values = c('gray','black')) +
    scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_pse_exp1

plot JND

plot_jnd_exp1 <- ggplot(mpars_exp1,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  labs(x = " ", y = "Mean JND (ms)") +
  coord_cartesian(ylim = c(0,400))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) + theme(legend.position = "none")

plot_jnd_exp1

ANOVA and T-test

Anova_exp1_pse<- ezANOVA(data = par_exp1, dv= pse, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp1_pse
$ANOVA
NA
Anova_exp1_jnd<- ezANOVA(data = par_exp1, dv= jnd, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp1_jnd
$ANOVA
NA
Anova_exp1_slope<- ezANOVA(data = par_exp1, dv= slope, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp1_slope
$ANOVA
NA

Experiment 2

Range Frequency Theory

A particular focus is the distribution of stimuli within the sets to be judged. To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the frequency of the sets firstly.

sumfreq_exp2_sub1 <-  dat_exp2 %>% filter(NSub == 1) %>% group_by(cond, curDur) %>% summarise(count = n()) 
count_exp2 <- sum(sumfreq_exp2_sub1$count)/2
sumfreq_exp2_sub1$exp <- 'Exp2'
sumfreq_exp2_sub1$freq <- sumfreq_exp2_sub1$count/count_exp2*100
fig_exp2_sub1_dist <- ggplot(data=sumfreq_exp2_sub1, aes(x=curDur, y=count, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) + 
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme

fig_exp2_sub1_dist

mDist_exp2 <-  dat_exp2 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp2
plot_mDist_exp2 <- ggplot(mDist_exp2,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
  #geom_text(aes(label=paste("(",m_cDur,",",round(cDur_se),")") ),size=8, hjust=0.5, vjust=-2, color = 'black')+
  labs(x = " ", y = " ") +
  #coord_cartesian(ylim = c(0,1600))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black")
  )
if (saveFigure == TRUE){
  ggsave("figures/plot_mDist_exp2.png", plot_mDist_exp2, width = 5, height = 5.5)
}
plot_mDist_exp2

Fit psychometric functions

fits_exp2 = quickpsy(dat_exp2, x = curDur, k =RP, prob = .5, grouping = .(cond, NSub))

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fits_exp2_all = quickpsy(dat_exp2, x = curDur, k =RP, 
                         grouping = .(cond))
fits_exp2_all
NULL
# plot fitted function
plot_fit_exp2 <- plot(fits_exp2_all) + 
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())
Ignoring unknown aesthetics: x
plot_fit_exp2

Average fitted paramters and plot

par_exp2 = fits_exp2$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns

par_exp2$slope = 3/exp(par_exp2$pse/1000) #add slope

par_exp2
mpse_exp2 = par_exp2%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd), m_slope = mean(slope), n = n(),
            pse_se = sd(pse)/sqrt(n-1), 
            jnd_se = sd(jnd)/sqrt(n-1),
            slope_se = sd(slope)/sqrt(n-1)) 
mpse_exp2

Export for JASP

List all of the parameters for Exp2 and export data for JASP

exp2_jasp <- par_exp2%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(DF, c("DF_pse", "DF_jnd","DF_slope"), sep = "_")%>%
  separate(AF, c("AF_pse", "AF_jnd", "AF_slope"), sep = "_")

exp2_jasp

plot PSE

plot_pse_exp2 <- ggplot(mpse_exp2,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  geom_signif(comparisons=list(c("DF", "AF")), annotations="***", y_position = 1250, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean PSE (ms)") +
  coord_cartesian(ylim = c(0,1300))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_pse_exp2

plot JND

plot_jnd_exp2 <- ggplot(mpse_exp2,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  geom_signif(comparisons=list(c("DF", "AF")), annotations="***", y_position = 330, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean JND (ms)") +
  coord_cartesian(ylim = c(0,350))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_jnd_exp2

ANOVA

Anova_exp2_pse <- ezANOVA(data = par_exp2, dv= pse, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp2_pse
$ANOVA
NA
Anova_exp2_jnd <- ezANOVA(data = par_exp2, dv= jnd, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp2_jnd
$ANOVA
NA
Anova_exp2_slope <- ezANOVA(data = par_exp2, dv= slope, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp2_slope
$ANOVA
NA

Experiment 3

Range Frequency Theory

To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the distribution of stimuli within the sets firstly.

sumfreq_exp3_sub1 <-  dat_exp3 %>% filter(NSub ==1) %>% group_by(cond, curDur) %>% summarise(count = n()) 
# rename columns
sumfreq_exp3_sub1$exp <- 'Exp3'
count_exp3 <- sum(sumfreq_exp3_sub1$count)/2
sumfreq_exp3_sub1$freq <- sumfreq_exp3_sub1$count/count_exp3*100

fig_exp3_sub1_dist <- ggplot(data=sumfreq_exp3_sub1, aes(x=curDur, y=freq, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) + 
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme

fig_exp3_sub1_dist

mDist_exp3 <-  dat_exp3 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp3
plot_mDist_exp3 <- ggplot(mDist_exp3,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
   labs(x = " ", y = " ") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black"))
plot_mDist_exp3

Fit psychometric functions

fits_exp3 = quickpsy(dat_exp3, x = curDur, k =RP, prob = .5,
                     grouping = .(cond, NSub), thresholds = FALSE)

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fits_exp3_all = quickpsy(dat_exp3, x = curDur, k =RP, 
                         grouping = .(cond), thresholds = FALSE)
fits_exp3_all
NULL
# plot fitted function
plot_fit_exp3 <- plot(fits_exp3_all) +  
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

plot_fit_exp3

List all of the parameter for each subjects

par_exp3 = fits_exp3$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns

par_exp3$slope = 3/exp(par_exp3$pse/1000) #add slope

par_exp3
mpars_exp3 = par_exp3%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd), m_slope = mean(slope), n = n(),pse_se = sd(pse)/sqrt(n-1), jnd_se = sd(jnd)/sqrt(n-1),slope_se = sd(slope)/sqrt(n-1))

mpars_exp3

##Export for JASP

List all of the parameters for Exp3 and export data for JASP

exp3_jasp <- par_exp3%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(`U-shaped`, c("U_pse", "U_jnd", "U_slope"), sep = "_")%>%
  separate(`I T-shaped`, c("B_pse", "B_jnd", "B_slope"), sep = "_")

exp3_jasp

plot PSE

plot_pse_exp3 <- ggplot(mpars_exp3,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  coord_cartesian(ylim = c(0,1300)) +
  labs(x = " ", y = "Mean PSE (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())
plot_pse_exp3

plot JND

plot_jnd_exp3 <- ggplot(mpars_exp3,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  coord_cartesian(ylim = c(0,300))+
  geom_signif(comparisons=list(c("U-shaped", "I T-shaped")), annotations="***", y_position = 250, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean JND (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")
plot_jnd_exp3

ANOVA

Anova_exp3_pse<- ezANOVA(data = par_exp3, dv= pse, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp3_pse
$ANOVA
NA
Anova_exp3_jnd<- ezANOVA(data = par_exp3, dv= jnd, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp3_jnd
$ANOVA
NA
Anova_exp3_slope<- ezANOVA(data = par_exp3, dv= slope, wid=NSub, within=.(cond))
Converting "NSub" to factor for ANOVA.
Anova_exp3_slope
$ANOVA
NA

figures in manuscript

plot figure 1 in manuscript

fig_exp1_sub1_dist2 <- ggplot(data=sumfreq_exp1_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(),width = 3) + 
  geom_point()+
  xlab('') + ylab('Prob. (%)') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 5)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank()) + facet_wrap(~cond)

fig_exp2_sub1_dist_2 <- ggplot(data=sumfreq_exp2_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(), width = 3) + 
  geom_point()+
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 10)) +
  xlab('') + ylab('Prob. (%)') +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = 'none', legend.title = element_blank()) + facet_wrap(~cond)

fig_exp3_sub1_dist2 <- ggplot(data=sumfreq_exp3_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(), width = 3) + 
  geom_point()+
  xlab('Durations (ms)') + ylab('Prob. (%)') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 10)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+ facet_wrap(~cond)

plot_grid(fig_exp1_sub1_dist2, fig_exp2_sub1_dist_2, fig_exp3_sub1_dist2,  ncol = 1, labels = c("A", "B", "C"), rel_heights = c(3,3,3))

plot Figure 2 in manuscript

plot_grid(plot_fit_exp1, plot_pse_exp1, plot_jnd_exp1,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))

plot Figure 3 in manuscript

plot_grid(plot_fit_exp2, plot_pse_exp2, plot_jnd_exp2,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))

plot Figure 4 in manuscript

plot_grid(plot_fit_exp3, plot_pse_exp3, plot_jnd_exp3,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))

Model Results

load the Model result

#customize theme
theme_new <- theme_bw() + 
  theme(panel.border = element_blank(), 
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(), 
        axis.line=element_line(colour="black"),
        strip.background = element_rect(color = "white", fill = "white"),
        panel.grid = element_blank())
models <- c('model1', 'model2','model3', 'model4','model5')
expDat <- list(dat_exp1, dat_exp2, dat_exp3)
#load the data and remove the outliers
par_GLM_observed <-read.csv('../data/par_observed.csv') %>% filter(!((NSub == 10|NSub == 6 ) & (cond == 'AF'| cond =='DF')))%>% filter(!((NSub == 1) & (cond == 'PS'| cond =='NS')))
modelresults<- read.csv("../data/modelresults.csv")  %>% filter(!((NSub == 10|NSub == 6) & (cond == 'AF'| cond =='DF')))%>% filter(!((NSub == 1) & (cond == 'PS'| cond =='NS')))
displayModellist <- c("Bisection Model",  "Spacing Model", "Ensemble Mean",  "Two-stage Ensemble Mean", "EDA")
#combine oberserved and predicated PSEs and JNDs
par_comb = left_join(modelresults, par_GLM_observed, by = c('NSub', 'cond')) 
par_comb$errpse <- par_comb$PSEmap-par_comb$pse
par_comb$errjnd <- par_comb$JNDmap-par_comb$jnd
par_comb$model = factor(par_comb$model, labels = displayModellist)
head(par_comb)
NA
#calculate AIC and BIC
numParam <- 3
mpar_comb <- par_comb %>% dplyr::group_by(model, cond) %>%
  dplyr::summarise(sumerrpse=sum((errpse)^2), n=n(), 
                   sumerrjnd=sum((errjnd)^2)) %>% 
  dplyr::group_by(model, cond) %>%
  summarise(aicPse= 2 * numParam +  n*log(sumerrpse/n),
            bicPse = n*log(sumerrpse/n) + numParam*log(n),
            aicJnd= 2 * numParam +  n*log(sumerrjnd/n),
            bicJnd = n*log(sumerrjnd/n) + numParam*log(n), ) 

### show the mean in each model 
m_par <- modelresults %>% group_by(model, cond, NSub) %>%
  summarise(xmean= mean(xmean), xmeanhat= mean(xmeanhat))  %>%
  group_by(model, cond) %>%
  summarise(xmean= mean(xmean), xmeanhat= mean(xmeanhat)) 

plot figure 7 in manuscript

par_comb <- arrange(transform(par_comb,
                              cond=factor(cond,levels=c("PS","DF","U-shaped","NS","AF","I T-shaped"))),cond)

cbp1 <- c( "#CC79A7", "#F0E442", "#0072B2", "#E69F00", "#D55E00")
plt_ErrorScatter = ggplot(par_comb, aes(errpse, errjnd, color = model, shape = model)) + 
  geom_hline(yintercept = 0, linetype='dashed')+ geom_vline(xintercept = 0, linetype='dashed')+ 
  geom_point() +
  xlab('Prediction error in the PSEs (ms)')+ ylab('Prediction error in the JNDs (ms)')+
  scale_color_manual(values = cbp1) +
  scale_shape_manual(values=c(0, 1, 2, 8, 16))+
  facet_wrap(~cond)+
  theme_new+ theme(legend.position = 'top')

plt_ErrorScatter

plot figure 6 in manuscript

m_parcomb <- par_comb %>% dplyr::group_by(model, cond) %>%
  dplyr::summarise(mPSEmap=mean(PSEmap), pse = mean(pse), mJNDmap=mean(JNDmap),jnd = mean(jnd),
                   merrpse =mean(errpse), merrjnd = mean(errjnd),n=n(), 
                   PSEmap_se = sd(PSEmap)/sqrt(n-1), JNDmap_se = sd(JNDmap)/sqrt(n-1),
                   errpse_se =sd(errpse)/sqrt(n-1), errjnd_se =sd(errjnd)/sqrt(n-1)) 

m_par_observed <- par_GLM_observed %>% dplyr::group_by(cond) %>%
  dplyr::summarise(mpse=mean(pse), mjnd= mean(jnd), n=n(), 
                   pse_se =sd(pse)/sqrt(n-1), jnd_se =sd(jnd)/sqrt(n-1)) 
m_par_observed$mPSEmap<-m_par_observed$mpse 
m_par_observed$mJNDmap<-m_par_observed$mjnd 

m_parcomb2 <- arrange(transform(m_parcomb,
                                cond=factor(cond,levels=c("PS","DF","U-shaped","NS","AF","I T-shaped"))),cond)


fig_estimation = ggplot(m_parcomb2, aes(x=mPSEmap, y=mJNDmap, color = model)) + 
  geom_point(data =m_par_observed, aes(x = mpse, y =mjnd, size=2), width =2, shape =16, alpha = 0.5,  color = 'black') +
  geom_point(data = par_comb, aes(x = pse, y =jnd), alpha = 0.25, color = 'lightgray') +
  geom_point() +
  geom_errorbar(aes(ymax=mJNDmap+JNDmap_se, ymin=mJNDmap-JNDmap_se), size=0.6)+
  geom_errorbarh(aes(xmax=mPSEmap+PSEmap_se, xmin=mPSEmap-PSEmap_se),size=0.6)+
  ylab('Observed JNDs (ms)')+xlab('Observed PSEs (ms)') +
  scale_color_manual(values = cbp1) +
  theme_new+ theme(legend.position = 'top') + 
  facet_wrap(.~cond,  ncol=3)+
  scale_size(guide = 'none')
Ignoring unknown parameters: width
#+xlim(600,1200)+ylim(45,200)
fig_estimation

---
title: "Temporal bisection is influenced by ensemble statistics of the stimulus set (Data Analysis Report)"
author: "Xiuna Zhu"
date: "12 Februar 2019"
output:
  pdf_document: default
  html_notebook: default
  word_document: default
  html_document:
    df_print: paged
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, eval = TRUE)
source('dataana.R')
```
# Experiment 1 

positive skew condition (400, 504, 636, 800, 1008, 1270, and 1600 ms)

negative skew condition (400, 730, 992, 1200, 1366, 1496, and 1600 ms)

## Range Frequency Theory

To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the distribution of stimuli within the sets firstly. 
```{r}
sumfreq_exp1_sub1 <-  dat_exp1 %>% filter(NSub == 1) %>% group_by(cond, curDur) %>% summarise(count = n())
count_exp1 <- sum(sumfreq_exp1_sub1$count)/2
sumfreq_exp1_sub1$exp <- 'Exp1'
sumfreq_exp1_sub1$freq <- sumfreq_exp1_sub1$count/count_exp1*100

# rename columns
fig_exp1_sub1_dist <- ggplot(data=sumfreq_exp1_sub1, aes(x=curDur, y=count, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) +
  #geom_smooth(method="loess",se = FALSE)+
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme+ facet_wrap(~cond)

fig_exp1_sub1_dist
```
## plot the distribution of stimulus set
```{r}
mDist_exp1 <-  dat_exp1 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp1

plot_mDist_exp1 <- ggplot(mDist_exp1,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
  labs(x = " ", y = "Mean of Durations (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black"))

plot_mDist_exp1
```



## fit psychometric functions


```{r fit psychometric functions Exp Spacing}
fits_exp1 = quickpsy(dat_exp1, x = curDur, k =RP, prob = .5,
                     grouping = .(cond, NSub), thresholds = FALSE)
head(fits_exp1$thresholds)
```


```{r}
fits_exp1_all = quickpsy(dat_exp1, x = curDur, k =RP, prob = .5, grouping = .(cond))
fits_exp1_all
```


```{r, fig.cap= 'PSE: Bisection task performance in Experiment Spacing.'}
# plot fitted function
plot_fit_exp1 <- plot(fits_exp1_all) +  
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

plot_fit_exp1
```



```{r}
aic(fits_exp1_all)
```

```{r}
ypred(fits_exp1_all)
```

=======
##slope
From the equation of psychometric fuction (PF), we can easily obtained the point of subjective equality (PSE, $\alpha$) and just noticeable difference (JND). Notice, the JND is defined by the difference between thresholds P=0.5 and P=0.75, so we have 
$$JND = log3/ \beta$$
Therefore, 

$$\beta = 3 / e^{JND} $$
```{r}
exp1_all_thres<- fits_exp1_all$thresholds
exp1_all_thres$slope = 3/exp(exp1_all_thres$thre/1000) #slope
exp1_all_thres
```


```{r}
exp1_thres<- fits_exp1$thresholds
exp1_thres$slope = 3/exp(exp1_thres$thre/1000) #slope
exp1_thres
```



## list all of the parameter for each subjects
```{r fitted paramters exp1}
par_exp1 = fits_exp1$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns
par_exp1$slope = 3/exp(par_exp1$jnd/1000) #slope

par_exp1
```


```{r average fitted paramters}
mpars_exp1 = par_exp1%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd),  m_slope = mean(slope), n = n(),
            pse_se = sd(pse)/sqrt(n-1), 
            jnd_se = sd(jnd)/sqrt(n-1),
            slope_se = sd(slope)/sqrt(n-1)) 

mpars_exp1
```




=======
##Export for JASP

List all of the parameters for exp1 and export data for JASP
```{r}
exp1_jasp <- par_exp1%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(`PS`, c("PSC_pse", "PSC_jnd","PSC_slope"), sep = "_")%>%
  separate(`NS`, c("NSC_pse", "NSC_jnd","NSC_slope"), sep = "_")

exp1_jasp
```



## plot PSE
```{r}
plot_pse_exp1 <- ggplot(mpars_exp1,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  geom_signif(comparisons=list(c("PS", "NS")), annotations="*", y_position = 1150, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean PSE (ms)") +
  coord_cartesian(ylim = c(0,1300)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_pse_exp1
```

## plot JND
```{r}
plot_jnd_exp1 <- ggplot(mpars_exp1,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  labs(x = " ", y = "Mean JND (ms)") +
  coord_cartesian(ylim = c(0,400))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) + theme(legend.position = "none")

plot_jnd_exp1
```


## ANOVA and T-test

```{r}
Anova_exp1_pse<- ezANOVA(data = par_exp1, dv= pse, wid=NSub, within=.(cond))
Anova_exp1_pse
```



```{r}
Anova_exp1_jnd<- ezANOVA(data = par_exp1, dv= jnd, wid=NSub, within=.(cond))
Anova_exp1_jnd
```



```{r}
Anova_exp1_slope<- ezANOVA(data = par_exp1, dv= slope, wid=NSub, within=.(cond))
Anova_exp1_slope
```


# Experiment 2

## Range Frequency Theory

A particular focus is the distribution of stimuli within the sets to be judged.  To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the frequency of the sets firstly. 


```{r}
sumfreq_exp2_sub1 <-  dat_exp2 %>% filter(NSub == 1) %>% group_by(cond, curDur) %>% summarise(count = n()) 
count_exp2 <- sum(sumfreq_exp2_sub1$count)/2
sumfreq_exp2_sub1$exp <- 'Exp2'
sumfreq_exp2_sub1$freq <- sumfreq_exp2_sub1$count/count_exp2*100
fig_exp2_sub1_dist <- ggplot(data=sumfreq_exp2_sub1, aes(x=curDur, y=count, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) + 
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme

fig_exp2_sub1_dist
```
```{r}
mDist_exp2 <-  dat_exp2 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp2
plot_mDist_exp2 <- ggplot(mDist_exp2,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
  #geom_text(aes(label=paste("(",m_cDur,",",round(cDur_se),")") ),size=8, hjust=0.5, vjust=-2, color = 'black')+
  labs(x = " ", y = " ") +
  #coord_cartesian(ylim = c(0,1600))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black")
  )

plot_mDist_exp2
```



## Fit psychometric functions
```{r fit psychometric functions Exp2}
fits_exp2 = quickpsy(dat_exp2, x = curDur, k =RP, prob = .5, grouping = .(cond, NSub))
```


```{r}
fits_exp2_all = quickpsy(dat_exp2, x = curDur, k =RP, 
                         grouping = .(cond))
fits_exp2_all
```

```{r, fig.cap= 'PSE: Bisection task performance in Experiment 2'}
# plot fitted function
plot_fit_exp2 <- plot(fits_exp2_all) + 
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

plot_fit_exp2
```


## Average fitted paramters and plot
```{r list all of the parameter for each subjects}
par_exp2 = fits_exp2$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns

par_exp2$slope = 3/exp(par_exp2$pse/1000) #add slope

par_exp2
```

```{r}
mpse_exp2 = par_exp2%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd), m_slope = mean(slope), n = n(),
            pse_se = sd(pse)/sqrt(n-1), 
            jnd_se = sd(jnd)/sqrt(n-1),
            slope_se = sd(slope)/sqrt(n-1)) 
mpse_exp2
```

##  Export for JASP

List all of the parameters for Exp2 and export data for JASP
```{r}
exp2_jasp <- par_exp2%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(DF, c("DF_pse", "DF_jnd","DF_slope"), sep = "_")%>%
  separate(AF, c("AF_pse", "AF_jnd", "AF_slope"), sep = "_")

exp2_jasp
```


## plot PSE
```{r}
plot_pse_exp2 <- ggplot(mpse_exp2,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  geom_signif(comparisons=list(c("DF", "AF")), annotations="***", y_position = 1250, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean PSE (ms)") +
  coord_cartesian(ylim = c(0,1300))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_pse_exp2
```

## plot JND
```{r}
plot_jnd_exp2 <- ggplot(mpse_exp2,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  geom_signif(comparisons=list(c("DF", "AF")), annotations="***", y_position = 330, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean JND (ms)") +
  coord_cartesian(ylim = c(0,350))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_jnd_exp2
```




## ANOVA 

```{r}
Anova_exp2_pse <- ezANOVA(data = par_exp2, dv= pse, wid=NSub, within=.(cond))
Anova_exp2_pse
```


```{r}
Anova_exp2_jnd <- ezANOVA(data = par_exp2, dv= jnd, wid=NSub, within=.(cond))
Anova_exp2_jnd
```


```{r}
Anova_exp2_slope <- ezANOVA(data = par_exp2, dv= slope, wid=NSub, within=.(cond))
Anova_exp2_slope
```

# Experiment 3

## Range Frequency Theory

To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the distribution of stimuli within the sets firstly. 
```{r}
sumfreq_exp3_sub1 <-  dat_exp3 %>% filter(NSub ==1) %>% group_by(cond, curDur) %>% summarise(count = n()) 
# rename columns
sumfreq_exp3_sub1$exp <- 'Exp3'
count_exp3 <- sum(sumfreq_exp3_sub1$count)/2
sumfreq_exp3_sub1$freq <- sumfreq_exp3_sub1$count/count_exp3*100

fig_exp3_sub1_dist <- ggplot(data=sumfreq_exp3_sub1, aes(x=curDur, y=freq, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) + 
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme

fig_exp3_sub1_dist
```

```{r}
mDist_exp3 <-  dat_exp3 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp3
plot_mDist_exp3 <- ggplot(mDist_exp3,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
  labs(x = " ", y = " ") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black"))
plot_mDist_exp3
```


## Fit psychometric functions


```{r fit psychometric functions Exp3}
fits_exp3 = quickpsy(dat_exp3, x = curDur, k =RP, prob = .5,
                     grouping = .(cond, NSub), thresholds = FALSE)
```


```{r}
fits_exp3_all = quickpsy(dat_exp3, x = curDur, k =RP, 
                         grouping = .(cond), thresholds = FALSE)
fits_exp3_all
```



```{r, fig.cap= 'PSE: Bisection task performance in Experiment 3.'}
# plot fitted function
plot_fit_exp3 <- plot(fits_exp3_all) +  
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

plot_fit_exp3
```



## List all of the parameter for each subjects


```{r}
par_exp3 = fits_exp3$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns

par_exp3$slope = 3/exp(par_exp3$pse/1000) #add slope

par_exp3
```




```{r fitted paramters Exp3}
mpars_exp3 = par_exp3%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd), m_slope = mean(slope), n = n(),pse_se = sd(pse)/sqrt(n-1), jnd_se = sd(jnd)/sqrt(n-1),slope_se = sd(slope)/sqrt(n-1))

mpars_exp3
```


##Export for JASP

List all of the parameters for Exp3 and export data for JASP
```{r}
exp3_jasp <- par_exp3%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(`U-shaped`, c("U_pse", "U_jnd", "U_slope"), sep = "_")%>%
  separate(`I T-shaped`, c("B_pse", "B_jnd", "B_slope"), sep = "_")

exp3_jasp
```


## plot PSE
```{r}
plot_pse_exp3 <- ggplot(mpars_exp3,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  coord_cartesian(ylim = c(0,1300)) +
  labs(x = " ", y = "Mean PSE (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())
plot_pse_exp3

```

## plot JND
```{r}
plot_jnd_exp3 <- ggplot(mpars_exp3,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  coord_cartesian(ylim = c(0,300))+
  geom_signif(comparisons=list(c("U-shaped", "I T-shaped")), annotations="***", y_position = 250, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean JND (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")
plot_jnd_exp3
```




## ANOVA

```{r}
Anova_exp3_pse<- ezANOVA(data = par_exp3, dv= pse, wid=NSub, within=.(cond))
Anova_exp3_pse
```



```{r}
Anova_exp3_jnd<- ezANOVA(data = par_exp3, dv= jnd, wid=NSub, within=.(cond))
Anova_exp3_jnd
```



```{r}
Anova_exp3_slope<- ezANOVA(data = par_exp3, dv= slope, wid=NSub, within=.(cond))
Anova_exp3_slope
```

# figures in manuscript

## plot figure 1 in manuscript

```{r}
fig_exp1_sub1_dist2 <- ggplot(data=sumfreq_exp1_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(),width = 3) + 
  geom_point()+
  xlab('') + ylab('Prob. (%)') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 5)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank()) + facet_wrap(~cond)

fig_exp2_sub1_dist_2 <- ggplot(data=sumfreq_exp2_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(), width = 3) + 
  geom_point()+
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 10)) +
  xlab('') + ylab('Prob. (%)') +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = 'none', legend.title = element_blank()) + facet_wrap(~cond)

fig_exp3_sub1_dist2 <- ggplot(data=sumfreq_exp3_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(), width = 3) + 
  geom_point()+
  xlab('Durations (ms)') + ylab('Prob. (%)') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 10)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+ facet_wrap(~cond)

plot_grid(fig_exp1_sub1_dist2, fig_exp2_sub1_dist_2, fig_exp3_sub1_dist2,  ncol = 1, labels = c("A", "B", "C"), rel_heights = c(3,3,3))
```



## plot Figure 2 in manuscript
```{r}
plot_grid(plot_fit_exp1, plot_pse_exp1, plot_jnd_exp1,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))
```

## plot Figure 3 in manuscript
```{r}
plot_grid(plot_fit_exp2, plot_pse_exp2, plot_jnd_exp2,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))
```

## plot Figure 4 in manuscript
```{r}
plot_grid(plot_fit_exp3, plot_pse_exp3, plot_jnd_exp3,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))
```



# Model Results

## load the Model result

```{r}
#customize theme
theme_new <- theme_bw() + 
  theme(panel.border = element_blank(), 
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(), 
        axis.line=element_line(colour="black"),
        strip.background = element_rect(color = "white", fill = "white"),
        panel.grid = element_blank())
```

```{r}
models <- c('model1', 'model2','model3', 'model4','model5')
expDat <- list(dat_exp1, dat_exp2, dat_exp3)
#load the data and remove the outliers
par_GLM_observed <-read.csv('../data/par_observed.csv') %>% filter(!((NSub == 10|NSub == 6 ) & (cond == 'AF'| cond =='DF')))%>% filter(!((NSub == 1) & (cond == 'PS'| cond =='NS')))
modelresults<- read.csv("../data/modelresults.csv")  %>% filter(!((NSub == 10|NSub == 6) & (cond == 'AF'| cond =='DF')))%>% filter(!((NSub == 1) & (cond == 'PS'| cond =='NS')))
```

```{r}
displayModellist <- c("Bisection Model",  "Spacing Model", "Ensemble Mean",  "Two-stage Ensemble Mean", "EDA")
#combine oberserved and predicated PSEs and JNDs
par_comb = left_join(modelresults, par_GLM_observed, by = c('NSub', 'cond')) 
par_comb$errpse <- par_comb$PSEmap-par_comb$pse
par_comb$errjnd <- par_comb$JNDmap-par_comb$jnd
par_comb$model = factor(par_comb$model, labels = displayModellist)
head(par_comb)

```



```{r}
#calculate AIC and BIC
numParam <- 3
mpar_comb <- par_comb %>% dplyr::group_by(model, cond) %>%
  dplyr::summarise(sumerrpse=sum((errpse)^2), n=n(), 
                   sumerrjnd=sum((errjnd)^2)) %>% 
  dplyr::group_by(model, cond) %>%
  summarise(aicPse= 2 * numParam +  n*log(sumerrpse/n),
            bicPse = n*log(sumerrpse/n) + numParam*log(n),
            aicJnd= 2 * numParam +  n*log(sumerrjnd/n),
            bicJnd = n*log(sumerrjnd/n) + numParam*log(n), ) 

### show the mean in each model 
m_par <- modelresults %>% group_by(model, cond, NSub) %>%
  summarise(xmean= mean(xmean), xmeanhat= mean(xmeanhat))  %>%
  group_by(model, cond) %>%
  summarise(xmean= mean(xmean), xmeanhat= mean(xmeanhat)) 
```


## plot figure 7 in manuscript
```{r}
par_comb <- arrange(transform(par_comb,
                              cond=factor(cond,levels=c("PS","DF","U-shaped","NS","AF","I T-shaped"))),cond)

cbp1 <- c( "#CC79A7", "#F0E442", "#0072B2", "#E69F00", "#D55E00")
plt_ErrorScatter = ggplot(par_comb, aes(errpse, errjnd, color = model, shape = model)) + 
  geom_hline(yintercept = 0, linetype='dashed')+ geom_vline(xintercept = 0, linetype='dashed')+ 
  geom_point() +
  xlab('Prediction error in the PSEs (ms)')+ ylab('Prediction error in the JNDs (ms)')+
  scale_color_manual(values = cbp1) +
  scale_shape_manual(values=c(0, 1, 2, 8, 16))+
  facet_wrap(~cond)+
  theme_new+ theme(legend.position = 'top')

plt_ErrorScatter
```



## plot figure 6 in manuscript
```{r}
m_parcomb <- par_comb %>% dplyr::group_by(model, cond) %>%
  dplyr::summarise(mPSEmap=mean(PSEmap), pse = mean(pse), mJNDmap=mean(JNDmap),jnd = mean(jnd),
                   merrpse =mean(errpse), merrjnd = mean(errjnd),n=n(), 
                   PSEmap_se = sd(PSEmap)/sqrt(n-1), JNDmap_se = sd(JNDmap)/sqrt(n-1),
                   errpse_se =sd(errpse)/sqrt(n-1), errjnd_se =sd(errjnd)/sqrt(n-1)) 

m_par_observed <- par_GLM_observed %>% dplyr::group_by(cond) %>%
  dplyr::summarise(mpse=mean(pse), mjnd= mean(jnd), n=n(), 
                   pse_se =sd(pse)/sqrt(n-1), jnd_se =sd(jnd)/sqrt(n-1)) 
m_par_observed$mPSEmap<-m_par_observed$mpse 
m_par_observed$mJNDmap<-m_par_observed$mjnd 

m_parcomb2 <- arrange(transform(m_parcomb,
                                cond=factor(cond,levels=c("PS","DF","U-shaped","NS","AF","I T-shaped"))),cond)


fig_estimation = ggplot(m_parcomb2, aes(x=mPSEmap, y=mJNDmap, color = model)) + 
  geom_point(data =m_par_observed, aes(x = mpse, y =mjnd, size=2), width =2, shape =16, alpha = 0.5,  color = 'black') +
  geom_point(data = par_comb, aes(x = pse, y =jnd), alpha = 0.25, color = 'lightgray') +
  geom_point() +
  geom_errorbar(aes(ymax=mJNDmap+JNDmap_se, ymin=mJNDmap-JNDmap_se), size=0.6)+
  geom_errorbarh(aes(xmax=mPSEmap+PSEmap_se, xmin=mPSEmap-PSEmap_se),size=0.6)+
  ylab('Observed JNDs (ms)')+xlab('Observed PSEs (ms)') +
  scale_color_manual(values = cbp1) +
  theme_new+ theme(legend.position = 'top') + 
  facet_wrap(.~cond,  ncol=3)+
  scale_size(guide = 'none')
#+xlim(600,1200)+ylim(45,200)
fig_estimation
```

